Solving free surface fluid flow problems by the minimal kinetic energy functional

2001 ◽  
Vol 37 (5) ◽  
pp. 577-600 ◽  
Author(s):  
J. K. Lonyangapuo ◽  
L. Elliott ◽  
D. B. Ingham ◽  
X. Wen
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Kinetic Energy ◽  
Energy Functional ◽  
Flow Problems ◽  
Kinetic Energy Functional

The Introduction of Micro Cells to Treat Pressure in Free Surface Fluid Flow Problems

1995 ◽  
Vol 117 (4) ◽  
pp. 683-690 ◽  
Author(s):  
Peter E. Raad ◽  
Shea Chen ◽  
David B. Johnson
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Pressure Field ◽  
Flow Simulation ◽  
New Method ◽  
Computational Domain ◽  
Critical Feature ◽  
Flow Problems ◽  
Macro Cell ◽  
Marker And Cell Method

A new method of calculating the pressure field in the simulation of two-dimensional, unsteady, incompressible, free surface fluid flow by use of a marker and cell method is presented. A critical feature of the new method is the introduction of a finer mesh of cells in addition to the regular mesh of finite volume cells. The smaller (micro) cells are used only near the free surface, while the regular (macro) cells are used throughout the computational domain. The movement of the free surface is accomplished by the use of massless surface markers, while the discrete representation of the free surface for the purpose of the application of pressure boundary conditions is accomplished by the use of micro cells. In order to exploit the advantages offered by micro cells, a new general equation governing the pressure field is derived. Micro cells also enable the identification and treatment of multiple points on the free surface in a single surface macro cell as well as of points on the free surface that are located in a macro cell that has no empty neighbors. Both of these situations are likely to occur repeatedly in a free surface fluid flow simulation, but neither situation has been explicitly taken into account in previous marker and cell methods. Numerical simulation results obtained both with and without the use of micro cells are compared with each other and with theoretical solutions to demonstrate the capabilities and validity of the new method.

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